Journal ArticleDOI
Capacitated lot sizing with setup times
TLDR
In this paper, a Lagrangian relaxation of the capacity constraints of CLSP allows it to be decomposed into a set of uncapacitated single product lot sizing problems, which are solved by dynamic programming.Abstract:
This research focuses on the effect of setup time on lot sizing. The setting is the Capacitated Lot Sizing Problem (the single-machine lot sizing problem) with nonstationary costs, demands, and setup times. A Lagrangian relaxation of the capacity constraints of CLSP allows it to be decomposed into a set of uncapacitated single product lot sizing problems. The Lagrangian dual costs are updated by subgradient optimization, and the single-item problems are solved by dynamic programming. A heuristic smoothing procedure constructs feasible solutions (production plans) which do not require overtime. The algorithm solves problems with setup time or setup cost. Problems with extremely tightly binding capacity constraints were much more difficult to solve than anticipated. Solutions without overtime could not always be found for them. The most significant results are that (1) the tightness of the capacity constraint is a good indicator of problem difficulty for problems with setup time; and (2) the algorithm solve...read more
Citations
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Journal ArticleDOI
A double auction mechanism for coordinating lot-sizing in supply chains
TL;DR: An auction mechanism for the coordination of dynamic, uncapacitated lot-sizing problems in two-party supply chains where parties’ local data are private information and no external mediator is involved is presented.
Multi-Item capacitated lot-Sizing problem with setup times and shortage costs : Polyhedral results.
Nabil Absi,Safia Kedad-Sidhoum +1 more
TL;DR: In this article, a multi-item capacitated lot-sizing problem with setup times and shortage costs is addressed. But the problem is not solved in real-world production planning problems, since demand cannot be backlogged, but can be totally or partially lost.
Journal ArticleDOI
Reordenamento eficiente das colunas básicas na programação de lotes e cortes
TL;DR: In this paper, the combined problem of lot sizing and the cutting stock problem is considered, and a static reordering of the basic columns of the matrix of constraints is proposed to solve the problem.
Journal Article
A fast Lagrangian heuristic for large-scale capacitated lot-size problems with restricted cost structures
TL;DR: The results indicate that the cost assumption of increased productivity over time has dramatic effects on the problem sizes which are solvable, and it is demonstrated that general CLSP's can benefit greatly from applying the proposed heuristic.
Journal ArticleDOI
Predictive Search for Capacitated Multi-Item Lot Sizing Problems
TL;DR: In this paper , a predictive search method that integrates machine learning/advanced analytics, mathematical programming, and heuristic search into a single framework for capacitated multi-item lot sizing problems is proposed.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Journal ArticleDOI
Decomposition Principle for Linear Programs
George B. Dantzig,Philip Wolfe +1 more
TL;DR: A technique is presented for the decomposition of a linear program that permits the problem to be solved by alternate solutions of linear sub-programs representing its several parts and a coordinating program that is obtained from the parts by linear transformations.
Journal ArticleDOI
Dynamic Version of the Economic Lot Size Model
Harvey M. Wagner,T. M. Whitin +1 more
TL;DR: Disjoint planning horizons are shown to be possible which eliminate the necessity of having data for the full N periods and desire a minimum total cost inventory management scheme which satisfies known demand in every period.
Journal ArticleDOI
Validation of subgradient optimization
TL;DR: It is concluded that the “relaxation” procedure for approximately solving a large linear programming problem related to the traveling-salesman problem shows promise for large-scale linear programming.
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Solving multi-item capacitated lot-sizing problems using variable redefinition
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